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 A258038 Numbers prime(k) such that D(prime(k), k-1) < 0, where D( * , k-1) = (k-1)-st difference. 4
 7, 13, 19, 29, 37, 43, 59, 67, 73, 83, 97, 107, 113, 131, 139, 151, 163, 179, 191, 197, 211, 223, 229, 239, 251, 263, 271, 281, 293, 311, 317, 337, 349, 359, 373, 383, 397, 409, 421, 433, 443, 457, 463, 479, 491, 503, 521, 523, 547, 563, 571, 587, 599, 607 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Partition of the positive integers:  A258036, A258037; Corresponding partition of the primes: A258038, A258039. LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 FORMULA D(prime(k), k-1) = sum{(-1)^i prime(k-i)*C(k-i),i); i = 0..k-1} EXAMPLE D(prime(2), 1) = 3 - 2 > 0; D(prime(3), 2) = 5 - 2*3 + 2 > 0; D(prime(4), 3) = 7 - 3*5 + 3*3 - 2 < 0, so a(1) = prime(4) = 7; MATHEMATICA u = Table[Prime[Range[k]], {k, 1, 1000}]; v = Flatten[Table[Sign[Differences[u[[k]], k - 1]], {k, 1, 100}]]; w1 = Flatten[Position[v, -1]] (* A258036 *) w2 = Flatten[Position[v, 1]]  (* A258037 *) p1 = Prime[w1]  (* A258038 *) p2 = Prime[w2]  (* A258039 *) CROSSREFS Cf. A258036, A258037, A258039. Sequence in context: A211431 A299928 A096452 * A059647 A059310 A299929 Adjacent sequences:  A258035 A258036 A258037 * A258039 A258040 A258041 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 05 2015 STATUS approved

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Last modified September 20 17:16 EDT 2020. Contains 337265 sequences. (Running on oeis4.)